Intro to Phys Sci I Mechanics Heat Instructor Carlos Perez Important Physical Quantities in Classical Mechanics How fast do you need to walk to make it on time to your next class on campus When you throw a baseball straight up in the air how high does it go When a glass slips from your hand how much time do you have to catch it before it hits the oor These are the kinds of questions you will learn to answer in this course We are beginning our study of physics with mechanics the study of the relationships among force matter and motion There is some terminology we need to become familiar with before we start describing how and why objects move In this part of the course the concepts of physical system and frame of reference will be presented We will introduce important physical quantities such as time position displacement distance speed and velocity You have probably heard some of these terms before in regular conversations or when you drive your bike scooter car etc However the meanings these concepts take in physics are sometimes di erent from those in everyday use Clear de nitions are essential to developing clear explanations The language used by scientists di ers from our everyday language even though the ideas are related and the same words are used 1 Physical Systems and Models Physics is concerned with describing matter energy and interactions in nature in our universe The universe is so vast and complicated that a full description of all there is in it would be impossible That is why those of us who learn and do physics need to focus out attention on simpler collections of objects at a time By physical system we understand the part of the universe we are interested in analyzing and describing It can be an extended object a point particle a system of particles a rigid body the gas contained in a cylinder etc In physics a model is a simpli ed version of a physical system that would be too complicated to analyze in full detail For classical mechanics we will model physical systems as point particles unless explicitly stated What is a point particle A point particle is an idealized model that help us describe an extended system as a single point on the object or system As long as we focus our attention on that single point and describe how it behaves we can provide an accurate description of the real system The two gures below are examples of physical systems that can be modeled as point particles Figure 1 To simplify the analysis of a a baseball in ight we model it as b a point particle 1 Figure 2 We can select any point on a car and follow it through as the car moves This simpli es the description of the motion of each part of the car to describing just how that speci c point is moving We have several di erent choices for the point as seen in this gure where we present two of such choices 2 Frame of Reference To talk about positions distances velocities etc we will need a frame of reference We can think of a frame of reference as drawing an imaginary Cartesian coordinate system or grid on or over physical spaces Doing so allows us to have a sense of direction and coordinates in mathematical terms Remember that in order to have a Cartesian system we need an origin usually denoted by O and the directions what is positive and what is negative of three axes x y and z For our purposes we will work in up to two dimensions so we really need to de ne the x and y axes So how do frames of reference work Imagine a physical setting such as a football eld If we wanted to de ne a frame of reference for it we would have to pick what point on the eld represent the origin what direction the x axis points in and what direction the y axis follows There are few rules on how to do this except that the axes must be perpendicular to each other This freedom can let you simplify the analysis of certain situations or make your calculations much harder It is a matter of choosing wisely but the freedom to de ne your frame of reference is always there Here are some examples of how the frame of reference can be chosen for the football eld Figure 3 Two examples of frames of reference for a football eld We have freedom in choosing the origin and even the axes orientation We will try to de ne them such that we can make the analysis and calculations simpler 2 We can de ne a frame of reference for any or almost any physical setting that we will nd in this course Just think of how you would de ne a frame of reference for the classroom for your bedroom for a building on campus etc In all these examples both directions are horizontal However we can always choose one of the directions to be vertical This is typically done for cases like falling objects or projectiles where the y axis represent the vertical direction with positive y pointing up and negative y pointing down Figure 4 An example of a situation where one of the axes represent a horizontal direction x axis and the other axis a vertical direction y axis The origin was chosen to be the corner of the bedroom 3 Time We are all familiar with time This quantity literally dictates our everyday activities In our study of mechanics we will consider time to always be the independent variable in most experiments problems scenarios etc where this physical quantity plays a central role This means that other quantities will depend on time We can also think that the dependent variables are parametrized in terms of time However we really have no control over it time passes or keeps advancing regardless of our wishes actions etc A few technical details about time Time is a scalar quantity The notation we will typically use when doing math is t Time can be measured in seconds s minutes min hours h etc When a quantity is independent of time or doesn t change as time passes we say that it remains constant or unchanged The table below represents a set of measurements of an object s length that remains constant Time seconds Length m 1 2 5 4 6 5 1 5 1 5 1 5 1 5 3 4 Position The position of a system is a vector quantity used to describe the spatial location of such system with respect to the origin of a frame of reference In general the position is described by three coordinates one for each spatial dimension Don t worry we will work with up to two dimensions so we really need two coordinates or components or magnitude and angle to specify the location of an object completely One of the main goals of mechanics is to describe the position of a …